SlideShare a Scribd company logo
1 of 10
Download to read offline
PPR Maths nbk

                                MODUL 10
          SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT”
                      TOPIC : GRAPHS OF FUNCTIONS
                            TIME     : 2 HOURS

1.   a)        Complete Table 1 in the answer space for the equation y = 2x2 – 5x – 3.

     b)        For this part, use a graph paper.
               By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-
               axis, draw the graph of y = 2x2 – 5x – 3 for -3 ≤ x ≤ 5.

     c)        From your graph, find
               i)    the value of y when x = -2.4,
               ii)   the value of x when 2x2 – 5x – 3 = 0.

     d)        Draw a suitable straight line on your graph to find all the values of x which
               satisfy the equation 2x2 – 8x = 7 for -3 ≤ x ≤ 5.
               State these values of x.




     Answer:

     a)

           X          -3       -2   -1     0     0.5     1        2      3       4       5
           Y          30             4     -3            -6      -5      0       9      22
                                         Table 1



     c)         i)     y   =



                ii)    x   =




     d)         x =
PPR Maths nbk


2.    a)       Complete Table 2 in the answer space for the equation y = x2 – 5x + 4.

      b)       For this part, use a graph paper.
               By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-
               axis, draw the graph of y = x2 – 5x + 4 for 0 ≤ x ≤ 8.

      c)       From your graph, find
               a. the value of y when x = 4.5,
               b. the value of x when y = 21.75

      d)       Draw a suitable straight line on your graph to find all the values of x which
               satisfy the equation x2 – 7x + 3 = 0 for 0 ≤ x ≤ 8.
               State these values of x.



Answer:

      a)

           X          0       1    2      2.5      3      4      5      6       7        8
           Y          4       0   -2              -2             4      10      18      28
                                        Table 2



      c)        i)    y   =



                ii)   x   =




      d)        x =
PPR Maths nbk


                                                                                   5
3.    a)       Complete Table 3 in the answer space for the equation y = .
                                                                                   x

      b)       For this part, use a graph paper.
               By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the
                                                   5
               y-axis, draw the graph of y =         for -5 ≤ x ≤ 5.
                                                   x

      c)       From your graph, find
               a. the value of y when x = 1.8,
               b. the value of x when y = -6.

      d)       From your graph, find all the values of x with the condition that the value
               of y is three times the value of x.




Answer:

      a)

           X          -5        -3     -2    -1   -0.5   0.5    0.9    1.5   2.5       5
           Y          -1       -1.7   -2.5         -10   10     5.6    3.3             1
                                              Table 3



      c)        i)         y    =



                ii)        x    =




      d)        x =
PPR Maths nbk



                                                                            2
4.   a)       Complete Table 4 in the answer space for the equation y =
                                                                            x

     b)       For this part, use a graph paper.
              By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 1 units on the y-
                                            2
              axis, draw the graph of y =     for -4 ≤ x ≤ 4.
                                            x

     c)       From your graph, find
              a. the value of y when x = -1.5,
              b. the value of x when y = 1.2.

     d)       Draw a suitable straight line on your graph to find all the values of x which
                                     2  3
              satisfy the equation     = x - 2 for -4 ≤ x ≤ 4.
                                     x  4

              State these values of x.



     Answer:

     a)

          X      -4      -2.5   -2    -1   -0.5     0.5     1      2     2.5     4
          Y     -0.5     -0.8         -2    -4       4      2      1            0.5
                                       Table 4



     c)        i)    y    =



               ii)   x    =




     d)        x =
PPR Maths nbk



5.    a)       Complete Table 5 in the answer space for the equation
               y = x3 – 13x + 18 .

      b)       For this part, use a graph paper.
               By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-
               axis, draw the graph of y = x3 – 13x + 18 for -4 ≤ x ≤ 4.

      c)       From your graph, find
               a. the value of y when x = -1.5,
               b. the value of x when y = 25.

      d)       Draw a suitable straight line on your graph to find all the values of x which
               satisfy the equation x3 – 11x – 2 = 0 for -4 ≤ x ≤ 4.
               State these values of x.


Answer:

      a)

           X          -4       -3   -2   -1     0    1       2      3      4
           Y           6            36   30    18    6              6     30
                                          Table 5



      c)        i)         y   =



                ii)        x   =




      d)        x =
PPR Maths nbk



6.    a)       Complete Table 6 in the answer space for the equation
               y = x3 + x2 – 12x – 5.

      b)       For this part, use a graph paper.
               By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-
               axis, draw the graph of y = x3 + x2 – 12x – 5 for -4 ≤ x ≤ 4.

      c)       From your graph, find
               a. the value of y when x = 0.5,
               b. the value of x when 11.9.

      d)       Draw a suitable straight line on your graph to find all the values of x which
               satisfy the equation x3 + x2 – 10x = 0 for -4 ≤ x ≤ 4.
               State these values of x.



Answer:

      a)

           X          -4       -3   -2   -1     0    1       2      3      4
           Y          -5       13        7     -5   -15     -17           27
                                          Table 6



      c)        i)         y   =



                ii)        x   =




      d)        x =
PPR Maths nbk

                                       MODULE 10 – ANSWERS
                                    TOPIC: GRAPHS OF FUNCTIONS

1.         a) x=-2 y=15        x=0.5 y= -5     x=3 y=0

           b) graph


                                                    40




                                                    35




                                                    30




                                                    25
                                                                               y(x) = 2⋅x2-5⋅x-3

                                                         20.5
                                                    20




                                                    15
                                                                y(x) = 3⋅x+4


                                                    10




                                                    5




     -10                       -5                                                                  5        10
                                        -2.4    -0.75                                       4.75

                                                    -5




                                                   -10




           c) i)    x=-2.4 y= 20.5
              ii)   when 2x2 – 5x – 3 = 0
                                    y=0
                    Then the values of x is -0.5 and 3

           e) y=2x2-5x-3
              0=2x2-8x-7 (-)
              -----------------------
              Y= 3x + 4

                X    0    3
                Y    4    13

                From the graph x= -0.75 and 4.75
PPR Maths nbk


2.        a)x=2.5 y=-2.25                      x=4 y=0

          b)graph 2

          c)        i)         y=1.75
                    ii)        x=7.4

          e) straight line y=2x+1
             x=0.45 and 6.55


3.        a) x=-1 y=-5             x=2.5 y=2

          b)graph
                                                         16

                                                                                                    C
                                                         14


                                                         12


                                                         10
                                                              y(x) = 3⋅x

                                                         8


                                                         6


                                                         4


                                                         2


                                                                                                A
     -5        -4         -3              -2    -1              1          2   3     4      5
B
                                                         -2
                                           5
                                 y(x) =
                                           x             -4



                                                         -6


                                                         -8


                                                     -10



                                                     -12


                                                     -14




          c)        i)         x=1.8 y= 2.8
                    ii)        y=-6 x=-0.8

          e) The graph is y=3x

                    X     0 2
                    Y     0 6

                    The values of x= -1.3 and 1.3
PPR Maths nbk




4.   a)           x=-2 y=-1                    x=2.5 y=0.8

     b) graph

     c)           i)          y=-1.3
                  ii)         x=1.7

                                               3
     e) The straight line is y=                  x–2
                                               4

               The values of x = -0.75 and 3.45


5.   a) x=-3 y=30                x=2 y=0
     b) graph                                           45




                                                        40




                                                        35     34



                                                        30


                                                                                        y=x^3-1 3x+18

                                                        25




                                                        20


                                                                        y=-2x+20
                                                        15




                                                        10




                                                         5


                                                                                            3.85
                                  -3.2
                                                       -0.25
          -6             -4               -2                        2              3.35 4               6




c)   i)           x=-1.5 y=34                           -5


                  ii)    y=25            x=3.85

     e) y=x3-13x+18
        0=x3-11x-2              (-)
        --------------------------
        Y= -2x+20

               X 0 4
               Y 20 12
PPR Maths nbk

          X= -3.2, -0.25 and 3.35


6.   a)      x=-2 y=15     x=3 y=-5

     b) graph 6

     c)      i)     y=10.75
             ii)    x=-1.5

     e)      y=-12x-5

             x=-3.6, 0 and 2.75

More Related Content

What's hot

Add Math(F5) Graph Of Function Ii 2.1
Add Math(F5) Graph Of Function Ii 2.1Add Math(F5) Graph Of Function Ii 2.1
Add Math(F5) Graph Of Function Ii 2.1roszelan
 
Cbse Class 12 Maths Sample Paper 2012
Cbse Class 12 Maths Sample Paper 2012Cbse Class 12 Maths Sample Paper 2012
Cbse Class 12 Maths Sample Paper 2012Sunaina Rawat
 
Sslc maths-5-model-question-papers-english-medium
Sslc maths-5-model-question-papers-english-mediumSslc maths-5-model-question-papers-english-medium
Sslc maths-5-model-question-papers-english-mediummohanavaradhan777
 
Peperiksaan pertengahan tahun t4 2012 (2)
Peperiksaan pertengahan tahun t4 2012 (2)Peperiksaan pertengahan tahun t4 2012 (2)
Peperiksaan pertengahan tahun t4 2012 (2)normalamahadi
 
Form 4 formulae and note
Form 4 formulae and noteForm 4 formulae and note
Form 4 formulae and notesmktsj2
 
April 9, 2015
April 9, 2015April 9, 2015
April 9, 2015khyps13
 

What's hot (19)

Add Math(F5) Graph Of Function Ii 2.1
Add Math(F5) Graph Of Function Ii 2.1Add Math(F5) Graph Of Function Ii 2.1
Add Math(F5) Graph Of Function Ii 2.1
 
Cbse Class 12 Maths Sample Paper 2012
Cbse Class 12 Maths Sample Paper 2012Cbse Class 12 Maths Sample Paper 2012
Cbse Class 12 Maths Sample Paper 2012
 
Função quadrática
Função quadráticaFunção quadrática
Função quadrática
 
Escola naval 2017
Escola naval 2017Escola naval 2017
Escola naval 2017
 
IME 2018 - fechada
IME 2018 - fechadaIME 2018 - fechada
IME 2018 - fechada
 
AMU - Mathematics - 2007
AMU - Mathematics  - 2007AMU - Mathematics  - 2007
AMU - Mathematics - 2007
 
Sslc maths-5-model-question-papers-english-medium
Sslc maths-5-model-question-papers-english-mediumSslc maths-5-model-question-papers-english-medium
Sslc maths-5-model-question-papers-english-medium
 
0308 ch 3 day 8
0308 ch 3 day 80308 ch 3 day 8
0308 ch 3 day 8
 
Inequações
InequaçõesInequações
Inequações
 
10.1
10.110.1
10.1
 
0307 ch 3 day 7
0307 ch 3 day 70307 ch 3 day 7
0307 ch 3 day 7
 
Algebra1
Algebra1Algebra1
Algebra1
 
MATH : EQUATIONS
MATH : EQUATIONSMATH : EQUATIONS
MATH : EQUATIONS
 
Peperiksaan pertengahan tahun t4 2012 (2)
Peperiksaan pertengahan tahun t4 2012 (2)Peperiksaan pertengahan tahun t4 2012 (2)
Peperiksaan pertengahan tahun t4 2012 (2)
 
Form 4 formulae and note
Form 4 formulae and noteForm 4 formulae and note
Form 4 formulae and note
 
Polinômios 1
Polinômios 1Polinômios 1
Polinômios 1
 
Sistemas lineares 2
Sistemas lineares 2Sistemas lineares 2
Sistemas lineares 2
 
Add Maths 2
Add Maths 2Add Maths 2
Add Maths 2
 
April 9, 2015
April 9, 2015April 9, 2015
April 9, 2015
 

Similar to PPR Maths Graphs of Functions

Xmss ict lesson sec 2 qe wksheet
Xmss  ict lesson sec 2 qe wksheetXmss  ict lesson sec 2 qe wksheet
Xmss ict lesson sec 2 qe wksheetbryan
 
Integration worksheet.
Integration worksheet.Integration worksheet.
Integration worksheet.skruti
 
chapter1_part2.pdf
chapter1_part2.pdfchapter1_part2.pdf
chapter1_part2.pdfAliEb2
 
Nbhm m. a. and m.sc. scholarship test 2009
Nbhm m. a. and m.sc. scholarship test 2009Nbhm m. a. and m.sc. scholarship test 2009
Nbhm m. a. and m.sc. scholarship test 2009MD Kutubuddin Sardar
 
Sin cos questions
Sin cos questionsSin cos questions
Sin cos questionsGarden City
 
Sin cos questions
Sin cos questionsSin cos questions
Sin cos questionsGarden City
 
Midterm Study Guide
Midterm Study GuideMidterm Study Guide
Midterm Study Guidevhiggins1
 
Nbhm m. a. and m.sc. scholarship test 2007
Nbhm m. a. and m.sc. scholarship test 2007 Nbhm m. a. and m.sc. scholarship test 2007
Nbhm m. a. and m.sc. scholarship test 2007 MD Kutubuddin Sardar
 
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...Thomas Ong
 
Y11+gdc+maximize+your+use+of+the++ev+2
Y11+gdc+maximize+your+use+of+the++ev+2Y11+gdc+maximize+your+use+of+the++ev+2
Y11+gdc+maximize+your+use+of+the++ev+2estelav
 
Pc12 sol c03_ptest
Pc12 sol c03_ptestPc12 sol c03_ptest
Pc12 sol c03_ptestGarden City
 
AA Section 6-3
AA Section 6-3AA Section 6-3
AA Section 6-3Jimbo Lamb
 
Review for the Third Midterm of Math 150 B 11242014Probl.docx
Review for the Third Midterm of Math 150 B 11242014Probl.docxReview for the Third Midterm of Math 150 B 11242014Probl.docx
Review for the Third Midterm of Math 150 B 11242014Probl.docxjoellemurphey
 

Similar to PPR Maths Graphs of Functions (20)

Xmss ict lesson sec 2 qe wksheet
Xmss  ict lesson sec 2 qe wksheetXmss  ict lesson sec 2 qe wksheet
Xmss ict lesson sec 2 qe wksheet
 
C3 January 2012 QP
C3 January 2012 QPC3 January 2012 QP
C3 January 2012 QP
 
Integration worksheet.
Integration worksheet.Integration worksheet.
Integration worksheet.
 
chapter1_part2.pdf
chapter1_part2.pdfchapter1_part2.pdf
chapter1_part2.pdf
 
Nbhm m. a. and m.sc. scholarship test 2009
Nbhm m. a. and m.sc. scholarship test 2009Nbhm m. a. and m.sc. scholarship test 2009
Nbhm m. a. and m.sc. scholarship test 2009
 
Math cbse samplepaper
Math cbse samplepaperMath cbse samplepaper
Math cbse samplepaper
 
Mth 4108-1 c
Mth 4108-1 cMth 4108-1 c
Mth 4108-1 c
 
Mth 4108-1 c
Mth 4108-1 cMth 4108-1 c
Mth 4108-1 c
 
Sin cos questions
Sin cos questionsSin cos questions
Sin cos questions
 
Sin cos questions
Sin cos questionsSin cos questions
Sin cos questions
 
Midterm Study Guide
Midterm Study GuideMidterm Study Guide
Midterm Study Guide
 
Nbhm m. a. and m.sc. scholarship test 2007
Nbhm m. a. and m.sc. scholarship test 2007 Nbhm m. a. and m.sc. scholarship test 2007
Nbhm m. a. and m.sc. scholarship test 2007
 
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...
O Level A Maths Sec 3 Syallbus 2011 Simultaneous Equation, Indices, Surds, Ex...
 
Cs 71
Cs 71Cs 71
Cs 71
 
Y11+gdc+maximize+your+use+of+the++ev+2
Y11+gdc+maximize+your+use+of+the++ev+2Y11+gdc+maximize+your+use+of+the++ev+2
Y11+gdc+maximize+your+use+of+the++ev+2
 
Pc12 sol c03_ptest
Pc12 sol c03_ptestPc12 sol c03_ptest
Pc12 sol c03_ptest
 
AA Section 6-3
AA Section 6-3AA Section 6-3
AA Section 6-3
 
Cs 60
Cs 60Cs 60
Cs 60
 
Review for the Third Midterm of Math 150 B 11242014Probl.docx
Review for the Third Midterm of Math 150 B 11242014Probl.docxReview for the Third Midterm of Math 150 B 11242014Probl.docx
Review for the Third Midterm of Math 150 B 11242014Probl.docx
 
9.7
9.79.7
9.7
 

More from guestcc333c

F4 11 Lines And Planes In 3 Dim
F4 11 Lines And Planes In 3 DimF4 11 Lines And Planes In 3 Dim
F4 11 Lines And Planes In 3 Dimguestcc333c
 
F4 10 Angles Of Elevation Dep
F4 10 Angles Of Elevation   DepF4 10 Angles Of Elevation   Dep
F4 10 Angles Of Elevation Depguestcc333c
 
F4 09 Trigonometry Ii
F4 09 Trigonometry IiF4 09 Trigonometry Ii
F4 09 Trigonometry Iiguestcc333c
 
F4 08 Circles Iii
F4 08 Circles IiiF4 08 Circles Iii
F4 08 Circles Iiiguestcc333c
 
F4 07 Probability I
F4 07 Probability IF4 07 Probability I
F4 07 Probability Iguestcc333c
 
F4 06 Statistics Iii
F4 06 Statistics IiiF4 06 Statistics Iii
F4 06 Statistics Iiiguestcc333c
 
F4 05 The Straight Line
F4 05 The Straight LineF4 05 The Straight Line
F4 05 The Straight Lineguestcc333c
 
F4 04 Mathematical Reasoning
F4 04 Mathematical  ReasoningF4 04 Mathematical  Reasoning
F4 04 Mathematical Reasoningguestcc333c
 
F4 02 Quadratic Expressions And
F4 02 Quadratic Expressions AndF4 02 Quadratic Expressions And
F4 02 Quadratic Expressions Andguestcc333c
 
F4 01 Standard Form
F4 01 Standard FormF4 01 Standard Form
F4 01 Standard Formguestcc333c
 
Probability Modul
Probability ModulProbability Modul
Probability Modulguestcc333c
 
P2 Earth As A Sphere Test
P2 Earth As A Sphere TestP2 Earth As A Sphere Test
P2 Earth As A Sphere Testguestcc333c
 
P2 Solid Geometry
P2  Solid GeometryP2  Solid Geometry
P2 Solid Geometryguestcc333c
 
P2 Plans & Elevation Test
P2  Plans & Elevation TestP2  Plans & Elevation Test
P2 Plans & Elevation Testguestcc333c
 
P2 Area Under A Graph Modul
P2  Area Under A Graph ModulP2  Area Under A Graph Modul
P2 Area Under A Graph Modulguestcc333c
 
Mathematics Keynotes 2
Mathematics Keynotes 2Mathematics Keynotes 2
Mathematics Keynotes 2guestcc333c
 
P1 Bearing Modul
P1 Bearing ModulP1 Bearing Modul
P1 Bearing Modulguestcc333c
 
Module 15 Plan And Elevation
Module 15 Plan And ElevationModule 15 Plan And Elevation
Module 15 Plan And Elevationguestcc333c
 

More from guestcc333c (20)

F4 Answer
F4 AnswerF4 Answer
F4 Answer
 
F4 11 Lines And Planes In 3 Dim
F4 11 Lines And Planes In 3 DimF4 11 Lines And Planes In 3 Dim
F4 11 Lines And Planes In 3 Dim
 
F4 10 Angles Of Elevation Dep
F4 10 Angles Of Elevation   DepF4 10 Angles Of Elevation   Dep
F4 10 Angles Of Elevation Dep
 
F4 09 Trigonometry Ii
F4 09 Trigonometry IiF4 09 Trigonometry Ii
F4 09 Trigonometry Ii
 
F4 08 Circles Iii
F4 08 Circles IiiF4 08 Circles Iii
F4 08 Circles Iii
 
F4 07 Probability I
F4 07 Probability IF4 07 Probability I
F4 07 Probability I
 
F4 06 Statistics Iii
F4 06 Statistics IiiF4 06 Statistics Iii
F4 06 Statistics Iii
 
F4 05 The Straight Line
F4 05 The Straight LineF4 05 The Straight Line
F4 05 The Straight Line
 
F4 04 Mathematical Reasoning
F4 04 Mathematical  ReasoningF4 04 Mathematical  Reasoning
F4 04 Mathematical Reasoning
 
F4 03 Sets
F4 03 SetsF4 03 Sets
F4 03 Sets
 
F4 02 Quadratic Expressions And
F4 02 Quadratic Expressions AndF4 02 Quadratic Expressions And
F4 02 Quadratic Expressions And
 
F4 01 Standard Form
F4 01 Standard FormF4 01 Standard Form
F4 01 Standard Form
 
Probability Modul
Probability ModulProbability Modul
Probability Modul
 
P2 Earth As A Sphere Test
P2 Earth As A Sphere TestP2 Earth As A Sphere Test
P2 Earth As A Sphere Test
 
P2 Solid Geometry
P2  Solid GeometryP2  Solid Geometry
P2 Solid Geometry
 
P2 Plans & Elevation Test
P2  Plans & Elevation TestP2  Plans & Elevation Test
P2 Plans & Elevation Test
 
P2 Area Under A Graph Modul
P2  Area Under A Graph ModulP2  Area Under A Graph Modul
P2 Area Under A Graph Modul
 
Mathematics Keynotes 2
Mathematics Keynotes 2Mathematics Keynotes 2
Mathematics Keynotes 2
 
P1 Bearing Modul
P1 Bearing ModulP1 Bearing Modul
P1 Bearing Modul
 
Module 15 Plan And Elevation
Module 15 Plan And ElevationModule 15 Plan And Elevation
Module 15 Plan And Elevation
 

PPR Maths Graphs of Functions

  • 1. PPR Maths nbk MODUL 10 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT” TOPIC : GRAPHS OF FUNCTIONS TIME : 2 HOURS 1. a) Complete Table 1 in the answer space for the equation y = 2x2 – 5x – 3. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = 2x2 – 5x – 3 for -3 ≤ x ≤ 5. c) From your graph, find i) the value of y when x = -2.4, ii) the value of x when 2x2 – 5x – 3 = 0. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2x2 – 8x = 7 for -3 ≤ x ≤ 5. State these values of x. Answer: a) X -3 -2 -1 0 0.5 1 2 3 4 5 Y 30 4 -3 -6 -5 0 9 22 Table 1 c) i) y = ii) x = d) x =
  • 2. PPR Maths nbk 2. a) Complete Table 2 in the answer space for the equation y = x2 – 5x + 4. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x2 – 5x + 4 for 0 ≤ x ≤ 8. c) From your graph, find a. the value of y when x = 4.5, b. the value of x when y = 21.75 d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x2 – 7x + 3 = 0 for 0 ≤ x ≤ 8. State these values of x. Answer: a) X 0 1 2 2.5 3 4 5 6 7 8 Y 4 0 -2 -2 4 10 18 28 Table 2 c) i) y = ii) x = d) x =
  • 3. PPR Maths nbk 5 3. a) Complete Table 3 in the answer space for the equation y = . x b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the 5 y-axis, draw the graph of y = for -5 ≤ x ≤ 5. x c) From your graph, find a. the value of y when x = 1.8, b. the value of x when y = -6. d) From your graph, find all the values of x with the condition that the value of y is three times the value of x. Answer: a) X -5 -3 -2 -1 -0.5 0.5 0.9 1.5 2.5 5 Y -1 -1.7 -2.5 -10 10 5.6 3.3 1 Table 3 c) i) y = ii) x = d) x =
  • 4. PPR Maths nbk 2 4. a) Complete Table 4 in the answer space for the equation y = x b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 1 units on the y- 2 axis, draw the graph of y = for -4 ≤ x ≤ 4. x c) From your graph, find a. the value of y when x = -1.5, b. the value of x when y = 1.2. d) Draw a suitable straight line on your graph to find all the values of x which 2 3 satisfy the equation = x - 2 for -4 ≤ x ≤ 4. x 4 State these values of x. Answer: a) X -4 -2.5 -2 -1 -0.5 0.5 1 2 2.5 4 Y -0.5 -0.8 -2 -4 4 2 1 0.5 Table 4 c) i) y = ii) x = d) x =
  • 5. PPR Maths nbk 5. a) Complete Table 5 in the answer space for the equation y = x3 – 13x + 18 . b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x3 – 13x + 18 for -4 ≤ x ≤ 4. c) From your graph, find a. the value of y when x = -1.5, b. the value of x when y = 25. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x3 – 11x – 2 = 0 for -4 ≤ x ≤ 4. State these values of x. Answer: a) X -4 -3 -2 -1 0 1 2 3 4 Y 6 36 30 18 6 6 30 Table 5 c) i) y = ii) x = d) x =
  • 6. PPR Maths nbk 6. a) Complete Table 6 in the answer space for the equation y = x3 + x2 – 12x – 5. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x3 + x2 – 12x – 5 for -4 ≤ x ≤ 4. c) From your graph, find a. the value of y when x = 0.5, b. the value of x when 11.9. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x3 + x2 – 10x = 0 for -4 ≤ x ≤ 4. State these values of x. Answer: a) X -4 -3 -2 -1 0 1 2 3 4 Y -5 13 7 -5 -15 -17 27 Table 6 c) i) y = ii) x = d) x =
  • 7. PPR Maths nbk MODULE 10 – ANSWERS TOPIC: GRAPHS OF FUNCTIONS 1. a) x=-2 y=15 x=0.5 y= -5 x=3 y=0 b) graph 40 35 30 25 y(x) = 2⋅x2-5⋅x-3 20.5 20 15 y(x) = 3⋅x+4 10 5 -10 -5 5 10 -2.4 -0.75 4.75 -5 -10 c) i) x=-2.4 y= 20.5 ii) when 2x2 – 5x – 3 = 0 y=0 Then the values of x is -0.5 and 3 e) y=2x2-5x-3 0=2x2-8x-7 (-) ----------------------- Y= 3x + 4 X 0 3 Y 4 13 From the graph x= -0.75 and 4.75
  • 8. PPR Maths nbk 2. a)x=2.5 y=-2.25 x=4 y=0 b)graph 2 c) i) y=1.75 ii) x=7.4 e) straight line y=2x+1 x=0.45 and 6.55 3. a) x=-1 y=-5 x=2.5 y=2 b)graph 16 C 14 12 10 y(x) = 3⋅x 8 6 4 2 A -5 -4 -3 -2 -1 1 2 3 4 5 B -2 5 y(x) = x -4 -6 -8 -10 -12 -14 c) i) x=1.8 y= 2.8 ii) y=-6 x=-0.8 e) The graph is y=3x X 0 2 Y 0 6 The values of x= -1.3 and 1.3
  • 9. PPR Maths nbk 4. a) x=-2 y=-1 x=2.5 y=0.8 b) graph c) i) y=-1.3 ii) x=1.7 3 e) The straight line is y= x–2 4 The values of x = -0.75 and 3.45 5. a) x=-3 y=30 x=2 y=0 b) graph 45 40 35 34 30 y=x^3-1 3x+18 25 20 y=-2x+20 15 10 5 3.85 -3.2 -0.25 -6 -4 -2 2 3.35 4 6 c) i) x=-1.5 y=34 -5 ii) y=25 x=3.85 e) y=x3-13x+18 0=x3-11x-2 (-) -------------------------- Y= -2x+20 X 0 4 Y 20 12
  • 10. PPR Maths nbk X= -3.2, -0.25 and 3.35 6. a) x=-2 y=15 x=3 y=-5 b) graph 6 c) i) y=10.75 ii) x=-1.5 e) y=-12x-5 x=-3.6, 0 and 2.75